Geometry

Two mathematicians have proved a long-standing conjecture that is a step on the way toward finding the worst shape for packing the plane.

By studying the geometry of model space-times, researchers offer alternative views of the universe’s first moments.

Mathematicians have disproved a major conjecture about the relationship between curvature and shape.

In 1940 André Weil wrote a letter to his sister, Simone, outlining his vision for translating between three distinct areas of mathematics. Eighty years later, it still animates many of the most exciting developments in the field.

Four mathematicians broke a 75-year-old record by finding a denser way to pack high-dimensional spheres.

Mathematicians think abstract tools from a field called symplectic geometry might help with planning missions to far-off moons and planets.

Mathematicians have struggled to prove Falconer’s Conjecture, a simple, but far-reaching, hypothesis about the distances between points. They’re finally getting close.

Mathematicians have illuminated what sets of points can look like if the distances between them are all whole numbers.

The French mathematician spent decades developing a set of tools now widely used for taming random processes.